Answered: Let T : R2 → P2 be a linear…

Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2. if T(u1) = 2x+1 and T(u2) = x^2 +1, find T([a b]) in terms of a and b.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 17CM

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Question

Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2. if T(u1) = 2x+1 and T(u2) = x^2 +1, find T([a b]) in terms of a and b. [Hint: First express b as a coordinate vector in the basis B.]

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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